Question: What is the sum of the seven smallest distinct positive integer multiples of 9?
Explanation: We are asked to calculate $9+18+27+\cdots+63$.  Factor out 9 and use the identity $1+2+3+\cdots+n=\frac{n(n+1)}{2}$ to find that $9+18+\cdots+63=9(1+2+\dots+7)= 9 \cdot \frac{7 \cdot 8}{2} = \boxed{252}$.